1. Field of the Invention
The invention generally relates to systems and methods for the analysis of absorption of molecules onto solid surfaces. More specifically, the invention relates to methods and systems that use optical methods (e.g. ellipsometry) to determine information related to the adsorption process.
2. Description of the Relevant Art
The adsorption of macromolecules, colloids, and bioparticles to solid surfaces has been widely reported in literature with studies that include different methodologies, surfaces, and applications. The time-dependence nature of the adsorption processes, as well as the significance of the initial steps for various biomedical and industrial applications, highlights the importance of kinetic studies. Regardless of the selected analytical technique to follow the process, there are two main experimental approaches to study adsorption kinetics of particles: batch and flow experiments. Batch experiments are generally performed by monitoring the depletion of adsorbate in a dispersion of sorbent particles. Although this approach is attractive due to its minimal instrumental requirements, it involves non-uniform hydrodynamic conditions, and is limited to slow adsorption processes (significantly slower than the mixing and separation time).
A more efficient way to study adsorption processes, particularly those involving shorter time-scales, is by flowing a solution of adsorbate over the sorbent surface. Several authors have pointed out the advantages of performing such studies in which the well-controlled hydrodynamic conditions allow accurate measurements, particularly regarding the initial stages of the adsorption/desorption phenomena. Various flow displacement geometries have been used for such adsorption studies. Among those, setups yielding stagnation point flow conditions are frequently used for measurement of adsorption kinetics. Stagnation point flow conditions may be obtained by perpendicular impinging a jet of solution to the sorbent surface through a cylindrical channel. The stagnation point is defined as the intersection of the symmetry axis of the cylinder with the surface. The main advantage of this arrangement is that the hydrodynamics of the mass flux at the stagnation point can be accurately described. Additionally, under stagnation conditions, information regarding the contribution of each component involved in the adsorption process can be obtained.
Stagnation point flow conditions have been used for adsorption studies in conjunction with several techniques such as microscopy, quartz crystal microgravimetry, evanescent wave light scattering, and reflectometry. Spectroscopic ellipsometry (SE) is also used for adsorption studies because it can provide real-time information regarding the kinetics of the adsorption process as well as the structure of the adsorbed layer for a broad range of materials and substrates. Ellipsometry is an optical technique that measures changes in the reflectance and phase difference between the parallel (RP) and perpendicular (RS) components of a polarized light beam upon reflection from a surface. The intensity ratio of RP and RS can be related to the ellipsometric angles (Ψ, amplitude and Δ, phase difference as functions of wavelength or time) using Equation 1:
                                          tan            ⁡                          (              Ψ              )                                ⁢                      ⅇ                          /              Δ                                      =                              R            P                                R            S                                              Equation        ⁢                                  ⁢        1            
Spectroscopic ellipsometry allows the measurement of the ellipsometric angles as a function of the wavelength of the incident light beam. Because ellipsometry measures the ratio of two values originated by the same signal, the data collected are highly accurate and reproducible. The output values of ellipsometry are extremely sensitive to the thickness (down to the monolayer level), optical constants, and microstructure (such as surface roughness, index grading, and intermixing) of the films. This monolayer sensitivity is useful for real-time studies of film deposition, including the formation of layers of biological molecules on a wide variety of substrates. It is worth noticing that although dynamic adsorption studies performed by ellipsometry have been widely reported in literature, the flow conditions in these reports have not been properly characterized.
One common issue associated with the use of optical methods, such as reflectometry or ellipsometry, to perform adsorption kinetic studies is that these techniques typically underestimate the initial adsorption rate. The difference between the experimental and predicted values have been attributed to the fact that these instruments collect signals from a spot (few square millimeters) rather than an infinitesimal point (stagnation point). Therefore, the adsorption rates calculated based on these signals could be significantly smaller than the adsorption rates existing at the stagnation point. As a consequence, similar experiments performed with diverse experimental setups may render significantly different results (depending on the size of the measured area), making quantitative interlaboratory comparisons challenging.